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Outlier (spurious vector) is a common problem in practical velocity field measurement using particle image velocimetry technology (PIV), and it should be validated and replaced by a reliable value. One of the most challenging problems is to correctly label the outliers under the circumstance that measurement noise exists or the flow becomes turbulent. Moreover, the outlier's cluster occurrence makes it difficult to pick out all the outliers. Most of current methods validate and correct the outliers using local statistical models in a single pass. In this work, a vector field correction (VFC) method is proposed directly from a mixture statistical model of PIV signal. Actually, this problem is formulated as a maximum a posteriori (MAP) estimation of a Bayesian model with hidden/latent variables, labeling the outliers in the original field. The solution of this MAP estimation, i.e., the outlier set and the restored flow field, is optimized iteratively using an expectation-maximization algorithm. We illustrated this VFC method on two kinds of synthetic velocity fields and two kinds of experimental data and demonstrated that it is robust to a very large number of outliers (even up to 60 %). Besides, the proposed VFC method has high accuracy and excellent compatibility for clustered outliers, compared with the state-of-the-art methods. Our VFC algorithm is computationally efficient, and corresponding Matlab code is provided for others to use it. In addition, our approach is general and can be seamlessly extended to three-dimensional-three-component (3D3C) PIV data. [ABSTRACT FROM AUTHOR]